For the report of birth abroad be sure to include how you’ve spent time in the USA (I’d say 5 years proof is what the US govt wants.). If you went to a us college then showing transcripts would be enough to prove that I think.
I’d recommend marrying in Taiwan though. You’ll get legal protection in Taiwan and it will make things easier at a time where having a newborn will be enough of a learning curve.
For immigrating to the USA, you’d just need to go with your significant other to the USA, let her get a feel if she’d like it and then request to change her status from a visitor to the USA to a permanent resident.